Living in California, there are some strict rules about donating food and especially wild game... Most place will not accept such donations unless food has been FDA approved...
As you your comments on ethical killing... I am in full agreement. I don't know what an animal feels when it is in pain... But I know they don't like it, and I know I do not want to be the cause of unnecessary pain.
I am hunting purely for recreation... I do not have animals causing damage to my crops or business; so when I take an animal, I make a concerted effort to do so humanely.
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This information is very old and laws/ roles may have changed but years ago, when I was a deputy sheriff, I was sent on a call and it turned out the group had a deprivation permit to kill pigs in their orchard. Once the pigs were killed they were to be transported to the butcher and the meat was to go to the jail. It was 2:00 AM and I can not remember if the original call was for shots fired or something else. This was in Northern California.
You do need a tag to harvest wild pigs in California but I have no idea of their game status.